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Theoretical computer science

Exact derandomization of logarithmic space: \mathsf L=\mathsf{RL}=\mathsf{BPL}

OpenAI research collection · 1 manuscript · Source checked 2026-10-19

OpenAI's result summary

Proves \mathsf L=\mathsf{RL}=\mathsf{BPL}, resolving derandomization for bounded-error logarithmic-space computation. An effective compiler converts each randomized polynomial-time logarithmic-space machine deciding a language with one-sided or two-sided error into a deterministic logarithmic-space decider with explicit polynomial running-time bounds.

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MANUSCRIPT 01

Exact derandomization of logarithmic space: L = RL = BPL

We prove \mathsf L=\mathsf{RL}=\mathsf{BPL}, resolving the derandomization problem for polynomial-time randomized logarithmic space.

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